Depletion forces between silica surfaces in solutions ofpoly(acrylic acid)

Andrew J. Millinga and Brian Vincentba T he Birchall Centre for Inorganic Chemistry and Material Science, Keele University, Keele,Sta†ordshire, UK ST 5 5BGb School of Chemistry, University of Bristol, Bristol, UK BS8 1T S

The forces between silica surfaces in the presence of poly(acrylic acid) solutions have been measured as a function of polymerconcentration using an atomic force microscope. Under similar solution conditions to the forceÈdistance studies, the stability of acolloidal silica dispersion to depletion Ñocculation was studied. The measured forceÈdistance curves were used to interpret theobserved Ñocculation behaviour of the dispersion.

IntroductionWater-soluble polymers are used in many technological appli-cations, such as paint formulation, ceramic processing andwater treatment. Whereas the interfacial behaviour of electri-cally neutral polymers is regarded as being well understood1there is a paucity in the knowledge concerning the propertiesof polyelectrolyte molecules at interfaces and their subsequente†ects upon colloidal interactions. The Ñocculation of disper-sions by non-adsorbing (depleting) polyelectrolytes is one suchinstance that has received limited attention, boththeoretically2h4 and experimentally.5h8 In comparison to thecase of depleting uncharged polymer molecules where the(attractive) depletion interaction energy may be equated to theproduct of the polymer solution osmotic pressure and a deple-tion layer “overlapÏ volume9,10 (the depletion layer thicknessscaling according to the polymer segment correlationlength11), the depletion interaction due to polyelectrolyte mol-ecules is extremely complicated. The interaction now depends,inter alia, on the polyelectrolyte concentration, the solutionpH and ionic strength.

Recent developments in experimental techniques haveallowed direct measurement of the forces between colloidalparticles in the presence of polymer solutions. The Ðrst report-ed study of depletion forces due to non-adsorbing polymerswas of the depletion force between octadecylated silica sur-faces immersed in cyclohexane solutions of the neutralpolymer poly(dimethylsiloxane).12 Subsequently, the depletionforce between silica surfaces in aqueous solutions of the strongpolyelectrolyte sodium poly(styrene sulfonate) (NaPSS) wasstudied.13 Both of these studies were performed using atomicforce microscopy (AFM).

In this paper, we present data for the forces between silicasurfaces in the presence of a weak polyelectrolyte [poly(acrylicacid), PAA] in the absence of added electrolyte, measuredusing AFM. Additionally, it was observed that a colloidalsilica dispersion, under similar solution conditions as in theforceÈdistance studies, underwent destabilisation and sub-sequent restabilisation as the polyelectrolyte concentrationwas increased.

ExperimentalAll AFM experiments were performed using a Nanoscope IIIinstrument (Digital Instruments). The PAA sample used waskindly donated by N. F. C. Cawdrey ; details of the syntheticprocedure and characterisation are described elsewhere.14

Aqueous gel-permeation chromatography of the PAA samplegave a number-average molar mass of 111 000 g mol~1,(Mn)with a polydispersity index of 1.13. Polymer solutions(Mr/Mn

)were prepared using puriÐed water (ion-exchanged and ultra-Ðltered) of conductivity \0.5 lS cm~1 and pH measurementswere taken after brieÑy Ñushing the solutions with nitrogen.Silica spheres were obtained from Allied Signal and polishedsilica plates were purchased from H. A. Groiss. Contact modeAFM imaging of the plates gave a typical surface roughness of2 nm for a 1 lm2 scan size. Prior to use the plates weresoaked in 2 mol dm~3 and then, after washing withHNO3 ,copious amounts of puriÐed water, they were boiled inammoniacal hydrogen peroxide, as described by Trau et al.15Silica spheres of 4È6 lm radius were glued to the tips ofcalibrated16 AFM cantilevers (spring constant 0.07 N m~1,Digital Instruments) using Epikote 1004 resin (Shell), as out-lined by Ducker et al.17 In a typical AFM force measurementexperiment the deÑection of the cantilever is monitored usinga split photodiode as the Ñat surface is scanned towards andaway from it. Using the analysis of Ducker et al.,17 forceÈdistance curves may be constructed from the photodiode andscanner displacement data. For the forceÈdistance experi-ments, polymer solutions were introduced into the AFMliquid cell via a syringe and allowed to equilibrate for 15 minprior to acquisition of the data. Identical data were collectedin the instances when longer incubation times were allowed(ca. 4 h). ForceÈdistance scans were made using scanner dis-placements of 100È750 nm and scanning frequencies of 0.05È2Hz, both in the absence and presence of dissolved polymer.The data acquired were fully reversible with respect to solu-tion conditions. A silica sol with an average particle diameterof 80 ^ 8 nm was prepared using the method described bySto� ber et al.,18 as modiÐed by Bridger.19 Prior to use the solwas extensively dialysed against puriÐed water. Experimentsto determine the stability of the sols to Ñocculation were per-formed using sols (silica volume fraction 1%) and polymersolutions prepared gravimetrically. Flocculation of the solswas estimated by visual inspection, and stability loci were sub-sequently constructed.

Results and DiscussionAdsorption of PAA at the silica/water interface

The bulk-dissociation behaviour of PAA is illustrated in Fig.1, the gradient of the pH vs. log(concentration) line suggests2.7% dissociation of the monomer units, which in turn sug-gests a net excess charge of ca. 45 electrons molecule~1. The

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Fig. 1 Solution pH vs. log(concentration) of PAA [log(c)] in theabsence of added electrolyte

absorption of PAA onto silica over the pH range 3È7 has beeninvestigated previously by MacMillan.20 Within this range itmay be expected that both the silica surface and the PAAmolecules will be negatively charged. It was found that belowa pH of ca. 7, there was weak polymer adsorption (as shownby the adsorption isotherm,20 reproduced in Fig. 2). Presum-ably the adsorption is due to hydrogen bonding betweensilanol and carboxylate groups, this interaction overcomingthe electrostatic repulsion between the surface and thepolymer molecules. The roundness of the isotherms is thoughtto be due to the high polydispersity of the polymer sampleused.

Force–distance measurements

The presence of an adsorbed polymer layer, as suggested bythe adsorption isotherms, means that the analysis of the rawdata (scanner displacement and diode voltage), as describedin ref. 16, may not yield a true surface separation as thetotal force gradient [steric] electrical double-layer(EDL)] depletion] may exceed the cantilever spring con-stant, thus giving the appearance of compliance at a Ðnitesurface separation. However, in view of the very low amountof adsorbed polymer (ca. \0.2 mg m~1), it is expected that

Fig. 2 Adsorption isotherm for PAA g mol~1) onto(Mn\ 230 000

silica in the absence of added electrolyte ; the data were adapted fromref. 19

any such pseudo-compliance will occur at a true surfaceseparation of no more than a few nanometres. In all cases thecompliance gradient was more-or-less independent of thepolymer concentration, being the same (within experimentaluncertainty) as when simple electrolyte solutions were used.Thus, the forces estimated are not systematically a†ected bycompliance errors.

Fig. 3 presents measured reduced-forceÈdistance curves fora silica sphere interacting with a silica plate at various PAAconcentrations. There is no added electrolyte and the solutionpH corresponds to the data presented in Fig. 1. All the forcecurves exhibit some common features. These are : (i) at closesurface approach there is a monotonic repulsive force(primary maximum, (ii) upon increasing the surface1'¡ ) ;separation, h, there is a (secondary) minimum (iii) at(2&¡ ) ;even larger surface separations there is a secondary maximum(2'¡ ).

It is presumed that the initial repulsion at large h is due toEDL interactions between the silica surfaces in the presence ofinterstitial PAA. Upon further approach of the surfaces, theelectric Ðeld experienced by the interstitial polymer moleculesinduces them to vacate the interface region The(h \ 2'¡ ).depletion of the polymer coils reduces the interstitial osmoticpressure at the intersurface midplane relative to the bulkosmotic pressure, and the associated attractive depletion forceis initially dominant. However, upon further reduction in h theEDL contribution increases thereby creating the The2min¡ .

whilst resembling a typical EDL interaction, is compli-1max¡ ,cated by the Donnan equilibrium21 that is established tomaintain interstitial electroneutrality and the situation isfurther exacerbated by the presence of adsorbed polymerlayers. The e†ect of increasing polymer concentration is thatboth the apparent surface separation of the secondarymaximum and of the secondary minimum decrease, and thegradient of the primary maximum increases. The Ðrst two ofthese e†ects are illustrated in Fig. 4. The depth of the 2min¡initially increases, and then decreases, with increasing polymer

Fig. 3 ForceÈradius vs. distance curves for a silica sphere (radius 4.5lm) interacting with a silica plate in PAA solutions ; experimentaldata and theoretical Ðts (theoretical input parameters are(L) (…)given in Table 1). The bulk solution conditions are (a) 100 ppm, pH4.32 ; (b) 500 ppm, pH 3.74 ; (c) 1000 ppm, pH 3.50 ; and (d) 1500 ppm,pH 3.40.

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Fig. 4 The surface separation of the secondary maximum and thesecondary minimum (of the forceÈdistance curves) as a function ofpolymer concentration. The lines drawn are to guide the eye andsuggest that the depletion layer thickness is proportional to c~1@3 forc\ 1000 ppm.

concentration. At polymer concentrations greater than ca.1500 ppm the rapidly vanishes until at 2500 ppm the2min¡force curves are purely repulsive [see Fig. 5(a)]. The additionof electrolyte 2 ] 10~4 mol dm~3) completely elimi-(NaNO3 ,nated the This is a result of the reduction of the polymer2min¡ .solution osmotic pressure. A similar observation was made inan earlier study where NaPSS solutions13 were used.

The e†ect of adding NaOH to the polymer solution wasalso investigated. At low polymer concentrations (\1500ppm) this led to the disappearance of the presumably as2min¡ ,the silica surfaces became more highly charged and thus theEDL interactions overwhelmed any inter-surface disjoiningpressure due to polymer depletion. For higher polymer con-centrations, the force curves changed quite remarkably as thepH of the solution was raised. Fig. 5 illustrates the e†ect ofadding NaOH to a 2500 ppm PAA solution. The free-acidforce data show a monotonic repulsion. However, uponraising the pH to 4.91 two inÑections appear in the force curveat apparent surface separations of ca. 4 and 17 nm [points Aand B, Fig. 5(a)]. Further increase in pH exaggerates these

features, as the PAA coils gradually acquire a higher charge.At pH 6.62, the force curve is repulsive for all separations.Weak structural oscillations may be seen [points D and E,Fig. 5(b)]. The plateau-like force at close approach (point C)could be due to either elastic compression of the adsorbedpolymer layer inducing desorption of the adsorbed PAA orthe PAA layer assuming a more extended conformation andbehaving like a “brushÏ. For the latter case it has beenpredicted22 that the force between contacting brushes is con-stant, irrespective of surface separation. The force curve forpH 7.37 again shows the weak structural oscillations [pointsF and G, Fig. 5(c)], but upon closer approach the interactionresembles an EDL interaction and the polymer appears tohave desorbed (as suggested by the adsorption isothermresults). The period of the structural oscillation (DE or FG) isapproximately 21 nm, which falls roughly between the theo-retical hexagonal and cubic close-packing (for sphericalparticles) radius limits of 23.7 and 18.9 nm, respectively, thusthe PAA coils appear to be space-Ðlling at this concentration.This is in contrast to the structural force oscillations observedin NaPSS solutions13 (where the oscillatory period was lessthan the calculated mean space-Ðlling diameter per polymermolecule), and the X-ray scattering studies performed uponPAA solutions by Ise et al.23 [it should be noted that in thelatter instance the concentration of sodium poly(acrylate) was20 000 ppm] and the present results do not necessarily pre-clude the proposition of long-range attractive ion mediatedforces under certain conditions of surface charge and ionicstrength.24,25 Whilst the calculations of Dahlgren andLeermakers3 predict the presence of a depletion layer beyondan interface bearing an adsorbed polymer layer, the mean-Ðeld nature of their calculations means that the developmentof macrosolute structuring (or more strictly speaking, partialstructure factors) cannot be examined. Recently, Chatellierand Joanny4 have described analytical solutions for the inter-facial behaviour of weakly adsorbing, weak polyelectrolytemolecules at interfaces. Their calculations demonstrate thatnot only is a depletion layer beyond an adsorbed poly-electrolyte layer a possibility, but under certain solution con-ditions such as low background ionic strength, intermolecularstructure factors may develop in the interfacial region, leadingto damped oscillatory forces between two approaching sur-faces.

Our supposition that the observed long-range forcesbetween the two silica surfaces are due to a summation of theEDL and depletion forces are qualitatively supported by

Fig. 5 Log(forceÈradius) vs. distance curves for a silica sphere (radius 4.5 lm) interacting with a silica plate in PAA solutions as a function ofsolution pH at a bulk polymer concentration of 2500 ppm. (a) pH 3.36 (]), pH 4.91 (b) pH 6.62 ; (c) pH 7.37. The lines described on the pH(L) ;4.91, 6.62 and 7.37 data sets are to guide the eye.

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model calculations, which are presented in comparison to theexperimental data in Fig. 3. The depletion and EDL forces(ref. 10 and 26, respectively) between a sphere of radius a anda plate were calculated using eqn. (1) and (2).

Fdepletion\ pP(h ] 2a)(h [ 2D) (1)

FEDL \ 8peW02 a2C ih ] 2a

]1

(h ] 2a)2Dexp([ih) (2)

where e is the permittivity of the solution. The Ðtting param-eters used are the surface potential the interstitial Debye(W0),screening length (1/i) and the osmotic pressure of the polymersolution (P). The depletion layer thickness of polymer (D) wasassumed to be equivalent to half the surface separation of the

In the absence of added electrolyte, P was Ðrst estimated2max¡ .from the bulk pH measurements using RaoultÏs law, i.e., P \

(where is the hydrogen ion activity) and thenceRT CH`CH`

optimised. Full details of the Ðtting parameters used are givenin Table 1. These calculations represent an over-simpliÐcationof a complex system where there is an adsorbed poly-electrolyte layer (hence deÐning an e†ective plane-of-charge atthe interfaces is problematic), and we are neglecting short-range steric and van der Waals contributions to the inter-surface interaction. The simple EDL equation used does notaccount for variation of the local ionic strength (and hence theDebye screening length) either in the presence or absence offree polymer in solution (i.e., as the secondary maximum istraversed upon approach of the surfaces) and thus the Ðttingprocedure we have used is unable to reproduce detailed fea-tures of the secondary maximum. The force data presented inFig. 3 show very little evidence of any higher-order structurale†ects as discussed in a paper by Mao et al.27 This observ-ation lends some justiÐcation to the simplicity of the modelthat we have used in our data analysis. In principle, the Ðttedparameters could be used to calculate the virial coefficients ofa dispersion, providing suitable input data for equation-of-state approaches to colloidal phase separation.28 However,such data-Ðtting routines are extremely model-sensitive and itwould appear that direct integration of the force data couldprovide a more satisfactory approach. We are carrying outfurther investigations in this area. Another problem that pre-sents itself is the use of the Derjaguin approximation. WhilstCarnie and Stankovich29 have validated the use of thisapproximation in the interpretation of AFM EDL mediatedforce measurements between micrometre-sized spheres and aÑat plate, its applicability to a colloidal dispersion comprisingof nanometric particles is still questionable.

Flocculation studies

It was observed that addition of PAA to a silica dispersionresulted in both a lower Ñocculation boundary and an(C2`)upper restabilisation boundary with respect to increas-(C2``)ing polyelectrolyte concentration. The Ñoc phase formedappeared to be a weakly bound amorphous solid (as predictedby phase-equilibrium theories28 for low particle volumefractions) that could be readily broken up by gentle agitationof the container. Both diluting and increasing the polymerconcentration of a Ñocculated sol beyond the stability bound-aries resulted in restabilisation of the dispersion. In the region

Table 1 Input parameters for data Ðtting

c (ppm) pH Pa/Pa Pb/Pa D/nm W0/mV i~1/nm

100 4.32 115 110 87 55 40.2500 3.74 439 384 41.5 41 20.2

1000 3.52 727 495 37 43 17.21500 3.40 959 905 21.5 26 14.1

a Calculated using RaoultÏs relationship (T \ 290 K). b Fitted value.

where Ñocculation was observed there were always particles inthe supernatant Ñuid, suggesting that the is quite shallow2min¡throughout this range. Accounting for an estimated PAAadsorbed amount of 0.1 mg m~2, and the presence of deple-tion layers [from the position of the secondary maximum (Fig.4), the Ñocculation boundaries were calculated to be C2`\1100 ^ 50 ppm and ppm]. These relativelyC2``\ 1600 ^ 50high polymer concentrations, coupled with the weakness ofthe adsorption isotherm, and the observation that the AFMforce data were identical for both approach and retraction ofthe silica surfaces strongly suggest that polymer bridgingmechanisms are not responsible for the observed particulateÑocculation.

Additionally, the same polymer sample was used to inducedepletion Ñocculation of a polystyrene latex (mean particlediameter 500 nm) bearing a terminally grafted poly(ethyleneoxide) sheath.30 was found to be ca. 350 ppm, andC2` C2``ca. 750 ppm (pH 4; NaCl, 1 ] 10~4 mol dm~3). Compared tothe present data for the Ñocculation of the silica sol, the valuesof both and for the latex particles are lower. ThisC2` C2``is probably due to the larger particle diameter, and alsobecause the given (mean) polymer concentrations do notaccount for the presence of depletion layers which willincrease the e†ective (true) polymer concentration. Also,factors such as the surface charge of the particles must be con-sidered when comparing these two sets of results. Snowden etal., in a related study,8 observed simultaneous polymeradsorption and depletion Ñocculation in an experimentalsystem comprising a silica dispersion in the presence ofhydroxy cellulose ethers. In this instance the polymer usedwas electrically neutral and somewhat polydispersed.

ConclusionsThe forces of interaction between silica surfaces in the pres-ence of PAA solutions have been directly measured. There issimultaneous adsorption of PAA onto the silica surfaces and asecondary depletion layer is formed beyond the adsorbedlayer. This depletion layer leads to an attractive force betweenthe surfaces, which together with the repulsive EDL forcesforms an attractive well in the intersurface pair-potential.With increasing PAA concentration the width of the potentialwell decreases and the well-depth passes through a maximum.Flocculation studies showed the existence of sol destabi-lisation and subsequent restabilisation as the PAA concentra-tion was increased, in good qualitative agreement with theforce measurements. Clearly, the restabilisation of the sols isthermodynamic in origin, as opposed to kinetic stabilisationby a sufficiently high barrier in the interparticle pair-potential.31 The presence of depletion layers beyond anadsorbed polyelectrolyte layer, and the subsequent attractiveinteraction was Ðrst predicted by Dahlgren and Leermakers3using the ScheutjensÈFleer (SF) theory of polymers atinterfaces32,33 under non-equilibrium conditions (for equi-librium SF calculations the adsorbed layer would desorbupon close approach of the opposing surfaces). Similar predic-tions have been made recently by Chatellier and Joanny,4whose analytical equations for the interfacial behaviour ofweak polyelectrolyte solutions additionally forecast the possi-bility of macrosolute structuring near the interfacial region, asevidenced in this paper.

The invariance of the forceÈdistance scans with respect toscanning approach/retraction speed suggests that the hydro-dynamics of both solvent and free polymer interstitialdrainage34 does not a†ect the force data and the ion distribu-tion of the EDL may relax within the experimental timescalesallowed.

The destabilisation and subsequent restabilisation of a col-loidal silica dispersion with respect to increasing polymer con-centration are in agreement with the AFM force

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measurements, which represent the Ðrst direct measurement ofa depletion interaction due to a homopolymer in the presenceof surfaces bearing an adsorbed layer of the same polymer.

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Paper 7/01795B; Received 14th March, 1997

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